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I have several LC PDS network cards for my older LC's and they all have a socket which I assume is for an FPU... Given that I might be able to obtain said FPU for a few bucks, does anyone know what kind of FPU these things take?

I don't get it, if you're supposed to use the same FPU that fits the mac, AND you're not supposed to use the one on the card if your mac has an FPU, then why would they have a slot for an FPU? I mean if you have the FPU wouldn't you just put it in your mac? in what scenario would you put it in the card instead of your mac? Edit: I just looked at my LC, you can't put an FPU in an LC, and I assume this is true of the LCII as well. If this is the case, then could getting a network card with an FPU potentially speed up an LC/LCII?
– denodsterAug 21 '16 at 14:20

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@denodster: Yes, it's only for the LC and LC II, and because you can't put an FPU in those directly, you have to put them on a card. You can get a card with an FPU socket. But if you also want a network card, you need two cards, but there's just one card slot. Hence the combined network/FPU card, so you can have both.
– dirktAug 21 '16 at 17:23

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As a side note due the single PDS slot the LC cannot have a IIe card and ethernet at the same time. The IIe card does allow for extra floppy drives though.
– Michael ShopsinAug 22 '16 at 14:36

The reason is simple: so you don't have to choose between an FPU and a network card.

The Mac LC series (LC stands for "low cost") have no NuBus slots, but only a single PDS ("Processor Direct Slot"), and a 68020 or 68030 CPU which does not have an FPU. The PDS slot can be used to add one single extension card, usually an FPU or a network card. The Asante MCLC network card has a socket for an FPU so you can have both.

The puzzling comment in the documentation relates to other models such as the Mac IIci which already has a socket for the FPU on the mainboard. If you have an FPU on the mainboard and you add a second FPU on your ethernet card, neither of them will work properly and most likely the machine will not even boot at all.

Any 68882 in PLCC form factor should work (both the LC and LC II are 16MHz, I don't think you'll be able to find a 68882 rated less than 16MHz. Since the 68882 is a static design faster versions will work just fine at 16MHz).